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the first three terms of a geometric progression are 100,90 and 81 , the common ratio is 0.9
Find the sum to infinity of its terms ?
Can someone explain this step by step please as I do not understand
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The sum of the infinite geometric progression with the first term and the common ratio is
= ,
providing that |r| < 1.
If you are a school math student, you are not required to understand how this formula is obtained. Simply accept this fact and use this formula.
In your case = 100 and = 0.9.
Substitute these values into the formula. You will get
the infinite sum = = = 1000.
That's all. The infinite sum of this geometric progression is 1000.